To examine the behaviors of our model on the evolutions of the universe, we fit the models with the combination of
the CMB and Hubble constant data sets. The CMB data include temperature
and polarization angular power spectra from Planck 2018 with TT, TE, EE, low-\(l\)  polarization,
and CMB lensing from SMICA [1]}, [2]}, [3]}, [4]}, while the Hubble constant of \(H_0=74.03 \pm 1.42\)  \(\rm km\;s^{-1}Mpc^{-1}\)  is from Hubble Space Telescope (HST)  [5]}.
As we set \(s=0.25\)  and let the neutrino mass sum be a free parameter, both our model and \(\Lambda \) CDM contain seven free parameters, where the priors are listed in Table REF .
To obtain the best fitted values of cosmological parameters, we use the \(\chi ^2\)  method
with
\(\chi ^2 = {\chi ^2_{CMB}+ \chi ^2_{HST}} \,,\) 
